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A chain rule for nonsmooth composite functions via minimisation

Published online by Cambridge University Press:  17 April 2009

D. Ralph
D. Ralph
Affiliation:
Department of Mathematics, University of Melbourne, Parkville, Vic. 3052, Australia
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Abstract

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Nonsmooth calculus using the approximate subdifferential of Mordukhovich and loffe admits a sharper chain rule, hence sharper applications in optimisation, than does the generalised gradient of Clarke. We observe, however, that at a local minimum point of the composition of nonsmooth vector valued and real valued functions, the generalised gradient admits a special, relatively sharp chain rule, that yields sharper results than have been seen before in the context of the generalised gradient.

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 49 , Issue 1 , February 1994 , pp. 129 - 137
Copyright
Copyright © Australian Mathematical Society 1994

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